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The following results are extracted from the thesis of Antonello Nesci, and the interested reader is directed also to...
We present experimental and theoretical studies of optical fields with sub-wavelength features. We intend to gain a better understanding of the interaction of light with microstructures in order to determine their optical properties. An electromagnetic field is characterised by an amplitude, a phase and a polarisation state. Therefore, experimental studies require coherent detection methods, in particular heterodyne scanning probe microscope (heterodyne SNOM), which allow the measurement of amplitude and phase of the optical field with sub-wavelength resolution. We discuss some basic properties of phase distributions. Light waves diffracted by microstructures can give birth to phase dislocations, also called phase singularities. Phase singularities are isolated points where the amplitude of the field is zero. Phase dislocations can be observed in the near- and far-field of optical microstructures, such as gratings. The behaviour of phase singularities have been localised with a spatial resolution of 10 nm. Comparison of the calculated and measured amplitude and phase for the TE- and TM-mode with the heterodyne SNOM gives interesting information about the field conversion by the fibre tip probe. A non-trivial conclusion points out that the three vectorial components of the electric field are detected.
In figures 1 to 4, we present a description of the complete optical heterodyne probe system. We show how a heterodyne interferometer has been combined with a scanning probe optical microscope in order to measure amplitude and phase of optical near- and far-fields.
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Fig. 1: A laser beam is split into a signal and reference beam. The signal beam passes through two acousto optic modulators, creating an overall frequency difference of 70 kHz between signal and reference. This signal beam then illuminates the sample. The field generated by the sample is probed via the bent fibre tip, controlled using a commercial AFM system. The probed light then passes through a fibre and is combined with the reference, thus generating a beat signal at 70 kHz. This beat signal is detected, and the phase and amplitude extracted electronically.
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| Fig. 2 | Fig. 3 |
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Fig. 2: The laser beam exits downwards (from gold coloured box). It then passes
through the optical chopper (CH) and is split in two (BS). The reference is
injected into a fibre. The signal is passed through the two AOMs to shift its
frequency, and is then injected into a fibre.
Fig. 3: The signal arrives from the right via the fibre (yellow/green, bottom
right). The output passes via some in-line optics and is then directed to illuminate
the sample. The optical microscope is used to observe and position the fibre tip and
signal illumination relative to the sample. The tip position is controlled via the
commercial AFM (blue box, left). The resultant beat signal is measured using the
detector seen on the right. A perspex box surrounds this section of the SNOM, which
greatly improves stability.
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| (a) | (b) |
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Fig. 4: (a) direct illumination normal to sample plane. The light exits the
fibre (F), passes through a half-wave plate (H), a polariser (P) and
collimating lens. A mirror then reflects this light directly onto the sample.
(b) Frustrated Total Internal Reflection (RTIR). A prism is used to provide an
evanescent field for the sample. This evanescent field is perturbed by the presence of
the tip, and light then propagates into the tip and the connected signal fibre.
We study the amplitude and the phase of an optical plane wave. In Fig. 5 we can see the constant amplitude (colour scale) and the isophase contour plot.
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Fig. 5: Measurement of a plane wave propagating at a slight angle to the z-axis, towards the fibre tip. This is a real-space scan of the x-z plane, thus requiring combined movement of the tip in both x and z. The tip is assumed to be approximately aligned with the z-axis. Amplitude is time-averaged, and is thus constant for the whole plane. Heavy phase lines indicate multiples of two pi.
The behaviour of an evanescent wave has been studied. In fact, Photon Scanning Tunnelling Microscopy (PSTM) is essentially based on evanescent fields. Frustration of the evanescent field explains why and how the diffraction limit of a conventional optical microscope can be surpassed. 2-D measurements of an evanescent wave are shown in fig. 6 and in fig. 7 (cross-section of the absolute optical power, measured down to the femto-watt level!), revealing interesting phenomena in the near-field region, such as optical scattering from surface defects or dust (fig. 8).
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| Fig. 6 | Fig. 7 |
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Fig. 6: Measurement of the amplitude of the evanescent field generated via TIR at a
clean glass/air interface. The interface lies approximately in the z=0 plane.
Fig. 7: This evanescent field can be detected out to a distance of approximately one
micron (femto-Watt regime) before noise starts to become a significant problem.
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| (a) | (b) |
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Fig. 8: Near to the surface the amplitude (a) of the evanescent field dominates, and the measured phase (b) correlates with an evanescent wave. Further away, the amplitude of propagating components is now more prevalent, leading to phase information that describes propagation of scattered light away from the surface.
By mathematically adding a phase term in the reference arm, we can see the propagation of the light due to the scattering in the z-direction and the evanescent wavefront in the x-direction (movie 1).
After plane wave and evanescent wave detection, another test is also a source of interest: the evanescent standing wave (Figs. 9 (amplitude) and 10 (phase)). In fact, the interference of two evanescent waves, with opposite directions, allows our instrument to be characterised. Evanescent standing waves are a useful test "structure" because no topographical defect perturbs the detection (tip-surface forces).
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| Fig. 9 | Fig. 10 |
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Fig. 9: Evanescent standing wave field created by illuminating a
prism surface in TIR using two input beams coming from opposite directions. The scan
is in a single plane (x-y) parallel to the prism surface. The resulting field exhibits
periodically spaced regions of high and low amplitude (time-averaged), expected for a
standing wave field.
Fig. 10: The phase distribution for this field. The neighbouring regions of high
amplitude, separated by lines of near-zero amplitude, are always of opposite phase.
Amplitude and phase measurement of the sinusoidal modulation of the field enables investigation of the possible limitations of the device. Optical amplitude and phase changes with a resolution of 1.6 nm are presented in fig. 11.
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| (a) | (b) |
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One important goal of this work is the understanding of the interaction of light with microstructures. Even if the structure features are on the micron scale, the diffracted fields have sub-wavelength features. Sub-wavelength resolution measurements of the amplitude and phase of the optical fields generated by a micron pitch grating are shown in fig. 12. The Talbot effect, which is a representation of the grating at periodic distances, is also observed. The measurement has been made over a plane of 5 by 10 microns, demonstrating the high stability achieved with this apparatus.
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| (a) | (b) |
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Fig. 12: (a) Periodic nature of the field generated by a diffraction grating.
(b) Corresponding phase map. Phase remains very stable over the large area scanned,
indicating high stability of the equipment. The scan was finished when the tip finally
touched the sample, leading to distortion of the field for the values of z near the
surface.
By zooming in on a region of fig. 12, we can compare the calculation made with the Fourier Modal Method (fig. 13 a) with the measured phase (fig. 13 b).
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| (a) | (b) |
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We especially pay attention to the phase distribution behind the grating. Here, the interaction of light with microstructures gives birth to phase singularities. These special points, where the intensity vanishes, are a great source of interest. In fact, their position in space can give information on the original structure. The position of phase singularities has been measured with high resolution, even in the far-field, within 10 nm (Fig. 14).
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| (a) | (b) |
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One interesting behaviour of the phase distribution has been observed: during the propagation of the wavefront, the phase turns around the phase singularities, which remain at a fixed position. If the two phase singularities are close to each other, the phase turns with opposite directions around the phase singularity (movie 2).
Finally, we can see the propagation of the optical field behind a grating (1 micron pitch) in movie 3 which represents the amplitude multiplied by the cosine of the phase.
The measurement of the amplitude and phase in optical fields with sub-wavelength features has been demonstrated, opening a new area of research in nano-optics. In fact, such an instrument can be utilised in different domains. In future, we hope that coherent scanning probes can aid us in the understanding and the fabrication of optical nano-structures, such as photonic bandgap waveguides used in telecommunication devices.
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